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Prove that following i) 2.C(0)+5.C(1)+...

Prove that following
i) `2.C_(0)+5.C_(1)+8.C_(2)+…..+(3n+2)C_(n)=(3n+4).2^(n-1)`

A

`(4 -3n).2^(2n-1)`

B

`(4 - 3n).2^(n+1)`

C

`(4 + 3n).2^(n-1)`

D

`(2-3n).2^(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-BINOMIAL THEOREM-PRACTICE EXERCISE
  1. 1/2.""^10C0 -""^10C1 +2.""^10C2 - 2^2.""^10C3+…..+2^9. ""^10C10 =

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  2. ""^(2n +1)C0^2 -""^(2n+1)C1^2 + ""^(2n+1)C2^2 -…….- ""^(2n+1)C(2n+1)^2...

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  3. Prove that following i) 2.C(0)+5.C(1)+8.C(2)+…..+(3n+2)C(n)=(3n+4).2...

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  4. ""^20C0 + ""^20C1 + ""^20C2+…….+""^20C10 =

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  5. C1 + 2. C2 + 3. C3 + …... + n. Cn=

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  6. If ar is the coefficient of x^r in the expansion of (1+x)^n then a1/a0...

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  7. If (1+x)^n = C0 + C1 x+ C2 x^2 + ….....+ Cn x^n, then C0+2. C1 +3. C...

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  8. 1.""^20C1 - 2.""^20C2 + 3.""^20C3 - …..-20.""^20C20 =

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  9. (1+x+x^2 + ……+x^p)^n = a0 + a1x + a2 x^2 + ….+a(np) x^(np) rArr a1 + 2...

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  10. C1 + 4.C2 +7.C3 +…….+(3n-2).Cn=

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  11. sum(r=1)^(n) (-1)^(r-1) ""^nCr(a - r) =

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  12. 2.C0 + (2^2)/(2).C1 + (2^3)/(3).C2 + ……+(2^11)/(11).C10 =

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  13. ""^11C0^2 - ""^11C1^2 + ""^11C2^2 - ""^11C3^2 + ……- "^11C11^2 =

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  14. (C0)/(1) + (C2)/(3) + (C4)/(5) + ……+(C16)/(17) =

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  15. (C1)/(2) + (C3)/(4) + …….+(C15)/(16)=

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  16. The coefficient of x^3 in (1-4x)^(1//2) is

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  17. The range of x for which the expansion of (1-3/x)^(-3//4) is valid is

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  18. The range of x of which the expansion of (2-3x^2)^(-11/2)is valid is

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  19. The fifth term of (1 - (2x)/(3))^(3//4) is

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  20. For |x| lt 1, the (r + 1)^(th) term in the expansion of sqrt(1 - x) is

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